00:01
I feel like this video would be very long if i explain every little step.
00:04
So i'm just going to work it out the way i would do each problem.
00:08
And then hopefully you're on board with the final answer.
00:15
Just to keep this video so much short, because x or x plus one.
00:23
Because i'm going to just do both steps at once where the numbers that are in front become the exponents of each.
00:30
And then in order to combine them using addition, we write it as multiplication.
00:36
So it's going to be natural log of the quantity of x minus 1 squared, and the 1 half power is the same thing as the square root of x over x plus 1.
00:46
Now, i'm not sure if that simplifies at all, so i would just stop right there.
00:51
So moving on to b, problem number 12, a lot of the same thing, that we have log base 3 of 2x cubed and then minus i'll rewrite as one -third log base 3 of y, and then a plus 3 log base 3 of 1 minus z.
01:28
Really the same thing i'm going to talk about is all of the coefficients can become exponents, and then we can combine subtraction using division and addition using multiplication.
01:40
So log base 3 of 2x cubed over the y to the one -third power, which i would rewrite as the cube root of y.
01:51
And then that 1 minus z, because it's the plus, goes into the top cubed.
01:58
And then moving on to letter c, we have log of a plus b.
02:10
And plus log of a minus b and then minus log of a b.
02:24
And there's no coefficient this time, but we do have that plus and that minus.
02:29
So i would just leave my answer as log of a plus b times a minus b divided by a b.
02:40
And i don't believe that simplifies really much at all.
02:43
If anything, you can foil out on top and see that you have a squared minus b squared.
02:48
Over a, b.
02:51
I guess you could divide each one individually.
02:55
So it would be a log of a over b minus one of those bs against a b over a.
03:02
I don't know what the best answer is.
03:04
I probably would have stopped right there if you want my opinion.
03:07
And then moving on to 13...